Question

If the sum of first 8 and 9 terms of na a.P. Are 64 and 361. Find common difference and sum of its n terms

Answer 1

Answer:

64.22

Step-by-step explanation:

sum of 8 terms = 64

Sum of 9 term = 361

sum of 8 terms = (8/2) * ( a + a +7d)

=> 8a + 28d  = 64

=> 2a + 7d = 16   - eqA

Sum of 9 terms = (9/2)(a + a +8d)

=>  9a + 36d =  361   - eqB

2*eqB - 9EqA

=> 9d = 722 - 144

d = 578/9

d = 64.22

Answer 2

Answer:

• Sum of n terms in AP :

Sn = (n/2)[2a + (n- 1)d]

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⇒ S₈ = 64

⇒ 8/2 × (2a + 7d) = 64

⇒ 4 × (2a + 7d) = 64

⇒ 2a + 7d = 16 — eq. ( I )

⇒ S₁₉ = 361

⇒ 19/2 × (2a + 18d) = 361

⇒ 19 × (a + 9d) = 361

⇒ a + 9d = 19 — eq. ( II )

• Multiplying eq.( II ) by 2 & Subtracting from eq.( I ) from eq.( II ) :

↠ 2a + 18d - 2a - 7d = 38 - 16

↠ 11d = 22

↠ d = 2

• Substitute d value in eq. ( II ) :

⇒ a + 18 = 19

⇒ a = 19 - 18

⇒ a = 1

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⋆ Sum of nth terms of the AP :

↠ Sn = n/2 [2a + (n - 1)d]

↠ Sn = n/2 × [2 × 1 + (n - 1) × 2]

↠ Sn = n/2 × [2 + 2n - 2]

↠ Sn = n/2 × 2n

↠ Sn = n × n

↠ Sn = n²

∴ Sum of nth terms of the AP is n².